Exact solutions are obtained for transient torsio-nal responses of a finitely long,functionally graded hollowcylinder under three different end conditions,i.e.free-free,free-fixed and fixed-fixed.The cylinder with its externalsurface fixed is subjected to a dynamic shearing stress atthe internal surface.The material properties are assumedto vary in the radial direction in a power law form,whilekeep invariant in the axial direction.With expansion in theaxial direction in terms of trigonometric series,the govern-ing equations for the unknown functions about the radialcoordinate r and time t are deduced.By applying the var-iable substitution technique,the superposition method andthe separation of variables consecutively,series-form solu-tions of the equations are obtained.Natural frequencies andthe transient torsional responses are finally discussed for afunctionally graded finite hollow cylinder.
